Find the vector sum of three vectors `vecA, vecB and vecC,` using analytical method.

Explanation

Let `vecA, vecB and vecC` be represented in component from,
`vecA=vecA_(x)hati+vecA_(y)hatj+vecA_(z)hatk, vecB=vecB_(x)hati+vecB_(y)hatj+vecB_(z)hatk`
`vecC=vecC_(x)hati+vecC_(y)hatj+vecC_(z)hatk`
Let `vecD` be their summation vector,
`vecD=(vecA+vecB+veccC)`
`(vec(A_(x))hat(A_(y))hatj+vecA_(z)hatk)+(vec(B_(x))hati+vec(B_(y))hatj+vec(B_(z))hatk+vec(C_(x))hati+vec(C_(y))hatj+vec(C_(y))+vec(C_(z))hatk)`
Addition of vecotrs obey the the commutative as well as associative laurs.
`D=(A_(x)+B_(x)+C_(x))(2u sin theta)/(g)+(A_(y)+B_(y)+C_(y))hatj+(A_(z)+B_(z)+C_(z))hatk`
`+(A_(x)+B_(x)+C_(x))hati+(A_(y)+B_(y)+C_(y))hatj+(A_(z)+B_(z)+C_(z))(2usintheta)/(g)`
`D_(x)=A_(z)+B_(x)+C_(x), D_(y)=A_(y)+B_(y)+C_(y), D_(z)=A_(z)+B_(z)+C_(z)`